The complete derivation of \(\text{F}_x\)  is found in [1]}. Since the error state, in this paper, is extended to include sensor drift estimation \(\text{F}_x\)  is also extended as follows:
\(\text{F}_x = \frac{\partial f}{\partial \delta x} = \nonumber \\{\begin{bmatrix}\text{I}_3 & \text{I}_3 \Delta t & 0_3 & 0_3 & 0_3 & 0_3 & 0_3 & 0_3 \\0_3 & \text{I}_3 & - \text{R}\cdot \text{A} & - \text{R} \Delta t & 0_3 & \text{I}_3 \Delta t & 0_3 & 0_3 \\0_3 & 0_3 & \text{R}^T\lbrace \mathbf {\omega }\rbrace  & 0_3 & - \text{I}_3 \Delta t & 0_3 & 0_3 & 0_3 \\0_3 & 0_3 & 0_3 & \text{I}_3 & 0_3 & 0_3 & 0_3 & 0_3 \\0_3 & 0_3 & 0_3 & 0_3 & \text{I}_3 & 0_3 & 0_3 & 0_3 \\0_3 & 0_3 & 0_3 & 0_3 & 0_3 & \text{I}_3 & 0_3 & 0_3 \\0_3 & 0_3 & 0_3 & 0_3 & 0_3 & 0_3 & \text{I}_3 & 0_3 \\0_3 & 0_3 & 0_3 & 0_3 & 0_3 & 0_3 & 0_3 & \text{I}_3 \\\end{bmatrix}} \\\quad \text{A}=\left[(\textbf {a}_{mv} - \textbf {a}_b) \right]_\times \Delta t, \quad \mathbf {\omega } = (\mathbf {\omega }_{mv} - \mathbf {\omega }_b)\Delta t, \\\text{F}_w = \frac{\partial f}{\partial \textbf {w}} =\begin{bmatrix}0_3 & 0_3 & 0_3 & 0_3 \\\text{I}_3 & 0_3 & 0_3 & 0_3 \\0_3 & \text{I}_3 & 0_3 & 0_3 \\0_3 & 0_3 & \text{I}_3 & 0_3 \\0_3 & 0_3 & 0_3 & \text{I}_3 \\0_3 & 0_3 & 0_3 & 0_3 \\0_3 & 0_3 & 0_3 & 0_3 \\0_3 & 0_3 & 0_3 & 0_3\end{bmatrix}, \\{\text{Q}_{w} =\begin{bmatrix}\mathbf {\sigma }_v^2\Delta t ^ 2 \text{I}_3 & 0_3 & 0_3 & 0_3 \\0_3 & \mathbf {\sigma }_{\theta }^2 \Delta t ^ 2 \text{I}_3 & 0_3 & 0_3\\0_3 & 0_3 & \mathbf {\sigma }_a^2 \Delta t ^ 2 \text{I}_3 & 0_3 \\0_3 & 0_3 & 0_3 & \mathbf {\sigma }_{\omega }^2 \Delta t ^ 2 \text{I}_3\end{bmatrix}},\) 
